International Journal of Transportation Engineering,
Vol. 8/ No.2/ (30) Autumn 2020
149
IJTE, Vol. 8/ No.2/ (30) Autumn 2020, pp. 149-163
Research Paper
Analysis of Speed Profiles at an Unsignalised Intersection for
Left Turning Vehicles
Maryam Dolatalizadeh1, Amin Mirza Boroujerdian2*, Seyed Ehsan Seyed Abrishami3
Abstract
Intersections are one of the elements that play an important role in urban networks. Analysis of drivers’
performance at unsignalised intersections is crucial, especially in left-turning movements due to their several
inherent conflicts and variety of drivers’ maneuver types which affect traffic safety and capacity at such
intersections, so the purpose of this paper is to introduce how the behaviour of drivers will be specified in left-
turning at unsignalized intersection. For this study, traffic data were collected using a fixed digital camera.
First, the vehicle speed profiles are categorized into descending-ascending slope (type (A)), the smooth
descending-ascending slope (type (B)) and ascending slope (type (C)).The effects of the initial speed of left-
turning vehicles, the exposure with other vehicles, and the vehicle type (i.e., taxi versus other vehicles) are
investigated on the choice of speed profile. A multinomial logit model is utilized to explain how various
variables influence the choice of speed profile. The estimated model indicates that the initial speed and the
exposures are influential parameters. Also, vehicles with left exposure at intersections increase the drivers’
tendency for selecting type (A) profile while they have low to medium initial speeds when entering the
intersections. For the vehicles with high initial speeds, most drivers pass the intersection with type (B) profile.
Vehicles with low initial speeds and a low number of exposures increase the probability of selecting type (C)
profile. Introduced method can be applied for simulation models at unsignalised intersection to show how
drivers will behave in left-turning movements.
Keywords: Speed profile; unsignalised intersection; left turning; multinomial logit model
Corresponding author E-mail: [email protected]
1.Ph.D Candidate, Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran
2.Assistant Professor, Department of Civil and Environmental Engineering, Tarbiat Modares University,
Tehran, Iran.
3.Assistant Professor, Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
International Journal of Transportation Engineering,
Vol. 8/ No.2/ (30) Autumn 2020
150
1. Introduction
Intersections are one of the most important
elements in urban networks that a significant
portion of urban crashes fall at them whose safety
analysis should be taken into account to manage
safety in cities[Sun et al. 2012] or traffic
simulation. The simulation models use predicting
models of driver behaviour that can be a function
of vehicle, environment, road, and human factors.
The purpose of this paper is to introduce how the
behavior of drivers will be specified in left-
turning movement at unsignalized intersection, so
a method is introduced that uses a two-step
analysis to determine driving behaviour in
passing an unsignalised intersection, including
1.Categorizing of the vehicles' speed profiles,
2.Developing a multinomial logit model (MNL)
for selecting a speed profile. The main
contribution is the determinig of the speed
profiles in different conditions in the left turning
movement by drivers. The determining of turning
speed in microscopic model needs to calibrate
that the speed profiles and the results of this paper
can be used for this object. To indicate the
process of implementing the suggested method,
an urban unsignalised intersection is selected.
First, traffic data are collected with a digital
camera since this method provides the data
analysis with high accuracy at micro level. The
videos are analyzed with Kinovea software. The
coordinates of the left-turning vehicles from
minor to major approaches are extracted and the
speed profiles are drawn based on the movement
coordinates. Then, these speed profiles are
categorized into three types based on their shapes.
To obtain the effected variables in the choice of
the speed profiles, the MNL model is developed
on the data. The results show that the initial speed
(the left turning vehicle’s speed when entering
the intersection) and the exposures with left-
turning vehicles are effective. The results of the
presented method can be used in simulations for
predicting the movements at the intersections.
2. Literature Review
Previous studies on the current subject have
focused on drivers’ crossing behaviour at
unsignalised and signalised intersections.
Laureshyn, Åström and Brundell-Freij
[Laureshyn, Åström and Brundell-Freij, 2009]
classified speed profiles of left-turning vehicles at
a signalised intersection by pattern recognition
techniques (e.g., cluster analysis, supervised
learning, and dimension reduction).They
classified traffic conditions into three scenarios:
an observer that considered no on-coming traffic
pedestrians, driver yields to the on-coming
vehicles, and driver yields to the pedestrian
crossing. The results indicated that the pattern
recognition techniques have the capability to
classify speed profiles. Wolfermann,
Alhajyaseen, and Nakamura [Wolfermann,
Alhajyaseen, and Nakamura, 2011] evaluated
speed profiles of right and left-turning vehicles at
signalised intersections. They utilized the
regression model for modelling of speed,
acceleration, and jerk profiles. The results
showed that speed profiles are sensitive to
intersection layout, namely the approach angle,
the curb radius, and the position of the hard nose.
Also, the profiles had a random distribution that
depended on the approach of exit vehicle speed
and its lateral position in the exit. Platho, Groß
and Eggert [Platho, Groß and Eggert, 2013]
proposed an approach to predict the performance
in complex traffic situations. This method
evaluated driving situation for each vehicle that
stopped by the red traffic light, by leading
vehicle, and by intersection. Then, we employed
this information to select a specific model for
predicting its future velocity profile. Random
Forest Regression method was employed as a
prediction method. For prediction process of
Analysis of Speed Profiles at An Unsignalised Intersection for Left Turning Vehicles
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151
vehicle’s velocity profile, we employed some
features such as velocity and acceleration of that
vehicle, distance to stopping line of the next
relevant traffic light, relative velocity and relative
distance between that vehicle and its leading
vehicle, distance to the entry point of the next
intersection and time instance for predicting
velocity. Li et al. [Li et al. 2016] analyzed the
characteristics of conflict between left-turning
vehicles and illegally crossing pedestrians in the
affected region at signalised intersection. Four
modes of driving behaviour of left-turning
vehicles were considered that included crossing
at a uniform speed, crossing while decelerating,
crossing slowly, braking, and stopping. A cellular
automata model was used to simulate the driving
behaviour and a logit model of the behaviour
mode choice was also developed to analyze the
relative share of each behaviour mode. The most
important factors used in the choice model
included the time required for a vehicle to cross
the intersection, the time required for an illegally
crossing pedestrian to cross the affected region
and the time required for a pedestrian to cross the
crosswalk. Finally, the microscopic
characteristics of driving behaviours (i.e.,
instantaneous velocities, locations, and headway
of individual vehicles) and the macroscopic
parameters of traffic flow (i.e., average flow,
density, and speed) were determined. Dias, Iryo-
Asano and Oguchi [Dias, Iryo-Asano and
Oguchi, 2017] estimated the path of left-turning
vehicles at signalised intersections based on
speed and acceleration profiles simultaneously.
Minimum-jerk theory was proposed to model
trajectories for turning vehicles. Variables,
including initial and final speeds, initial and final
accelerations, and the movement time were used
to solve the cost function in the theory. The
results showed that this modelling process
reproduced turning trajectories with reasonable
accuracy compared to the results of previous
studies. Ma et al. [Ma et al. 2017] developed a
two-dimensional simulation for turning
movement at mixed-flow intersection. They used
a three-layered, “plan-decision-action”,
framework to determine turning parameters.
First, trajectories were characterized, then driving
behaviour was selected among three alternatives
that included car-following, turning, and
yielding. Finally, acceleration and angular
velocity in left-turning movements were
calculated. The model improved the performance
of simulation from two aspects of traffic
efficiency and safety. Armand, Filliat and Ibanez-
Guzman [Armand, Filliat and Ibanez-Guzman,
2013] applied Gaussian Processes to model the
velocity profile that the driver follows as the
vehicle decelerates towards a stop intersection. It
was shown that Gaussian Processes are well
adapted for such an application, using data
recorded in real traffic conditions. Lu et al. [Lu et
al. 2015] studied crossing behaviour of straight-
moving drivers when they encountered other
straight-moving drivers at unsignalised
intersections with the logit model. The dependent
variable of the model was straight-moving
vehicle status (preemptive=1, yielding=0). The
survey indicated that the most significant
parameters that affected drivers’ decisions were
relative speed between the right vehicle and left
vehicles, the relative distance between the right
vehicle to the crossing point and the left vehicle
to the crossing point, and the relative distance
between the right and left vehicles. The results of
decision-making time indicated that the straight-
moving drivers from the right side completed
preemptive/yielding decisions at 1.3 s before
reaching the crossing point and this time for
drivers from the left side is equal to 1.1 s. The
most important parameter that influenced the
drivers’ decisions was the difference between the
speeds of two vehicles. Patil and Pawar [Patil and
Pawar, 2016] surveyed traffic parameters, such as
traffic composition, speed variations, lane
distribution, trajectories, conflict points, and
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
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pedestrian movements for unsignalised
intersections. The authors extracted speed values
from the intersections. The results showed that
the speed at inner lane was higher than outer lane
vehicles. Meanwhile, minor approach vehicles
decreased their speed or stopped many times.
Trajectories of two-wheelers were found to be
much flatter than the trajectories in the standard
conflict point diagram. Zhang, Qi, and Chen
[Zhang, Qi and Chen, 2016] evaluated left-
turning movements from minor road approach at
unsignalised intersections. The binary logistic
analysis showed that parameters such as slower
speed of vehicles on the major or minor road and
more lanes on the minor road could cause drivers
to select normal vehicle paths.
Liu et al. [Liu et al. 2016] investigated the
behaviour of two straight-moving vehicles from
an orthogonal direction at unsignalised
intersection whose study focused on drivers’ risk
perception. They used effective parameters in
drivers’ behaviour based on their previous study
Lu et al. [Lu et al. 2015] for developing models
of drivers’ risk perception by ANFIS. Then, a
model established by game theory to determine
the relationship between risk perception value
and vehicle movement strategies that included
acceleration, uniform motion, and deceleration.
Finally, vehicle speed and the distance from a
vehicle to the crossing point were calculated by
analyzing the Nash equilibrium strategy.
Li et al. [Li et al. 2019], Surveyed the drivers’
visual scanning behavior at signalized and
unsignalized intersections in china. The results
showed that in left turning, drivers near
signalized intersections had more frequent
glances at the left view mirror, fixated much
longer on the forward and rear view mirror area,
and had higher transition probabilities from near
left to far left. Compared with drivers’ scanning
patterns in left turning maneuver at signalized
intersections, drivers with higher situation
awareness levels would divide more attention to
the forward and right areas than at unsignalized
intersections.
The survey research of the past studies indicate
some methods and effective parameters to
evaluate driving behaviour at the intersections.
In this study, a simple method is presented to
extract behavioral model of drivers for such
intersections and for determining of the effective
parameters on the driving behaviour is used from
the previous researches. Table 1 shows the
studies investigating drivers’ behaviour at
signalised and unsignalised intersections.
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Table 1.Summary of previous studies on drivers’ behaviour at the intersection
Author
(Year) Problem Definition Methodology Conclusions
Signalised Intersection
Laureshyn,
Åström and
Brundell-
Freij (2009)
Classifying speed profiles
of left turning vehicles
Pattern
recognition
techniques
Proposed framework is well method for
classification of speed profiles
Wolfermann,
Alhajyaseen
and
Nakamura
(2011)
Modelling of speed profiles
of turning vehicles
Regression
models
Speed profiles are sensitive to intersection
geometry
Platho, Groß
and Eggert
(2013)
An approach for predicting
performance in complex
traffic situations
Two-stage
simulation
Development of a classifier for driving
situation and a regressor for velocity profile
prediction
Li et al
(2016)
Analyzing of conflict
between left-turning
vehicles and pedestrians
Cellular
Automata
model
Determination of microscopic characteristics
of driving behaviours and macroscopic
parameters of traffic flow
Dias, Iryo-
Asano and
Oguchi
(2017)
Prediction of path of left
turning vehicle
Minimum-jerk
theory
Modelling process reproduced turning
trajectories with a reasonable accuracy
Ma et al
(2017)
a two-dimensional
simulation for turning
movement at mixed flow
intersection
“plan-decision-
action”
framework
The model improved the performance of
simulation from two aspects of traffic
efficiency and safety
Unsignalised Intersection
Armand,
Filliat and
Ibanez-
Guzman
(2013)
Modelling of velocity
profile in stop intersection
approaches
Gaussian
Processes
Gaussian Processes are well adapted for data
recorded in real traffic conditions
Lu et al
(2015)
Surveying of behaviour of
straight movements with
together
Logit model
The most important parameter that
influenced the drivers’ decisions was the
difference between the speeds of the two
vehicles
Patil and
Pawar (2016)
Surveying of traffic
parameters at intersection
Descriptive
statistics
One of the most important conclusions was
that minor approach vehicles decreased their
speed or stopped many times
Zhang, Qi
and Chen
(2016)
Evaluation of left turning
movements from minor
road approach
Binary logistic
analysis
Slower speed of vehicles on major or minor
road and more lanes on minor road were
effective on choice of normal vehicle paths
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
International Journal of Transportation Engineering,
Vol. 8/ No.2/ (30) Autumn 2020
154
Liu et al
(2017)
Modelling crossing
behaviour of drivers at
unsignalised intersection
with consideration of risk
perception
Game theory Determining of vehicle speed and the
distance from a vehicle to the crossing point
3. Methodology
3.1 Data Collection
In this study, Vesaleshirazi-Bozorgmehr
intersection is selected in Tehran. This
intersection is a four-leg unsignalised intersection
whose approaches are perpendicular to each other
and there is a median, stop line and the pedestrian
crossing each of them. There are two lanes in
each of the minor approaches and three lanes in
each of the major approaches. The reason to
selecte this intersection was the looking for an
unsignalized intersection and taking video above
the intersection, and also all videos had to be
analyzed with image processing software and
also it was needed an uncongested unsignalized
intersection with high volume of left-turning
movements that there was a high building that it
could install the camera to take videos so this
intersection was the best choice among all other
choices. Figure 1 shows a view of both the
intended intersection and considered movements
for this research.
Figure 1. View of case study and tracked
movement at the intersection
There are different methods for collection of
traffic data, such as field observers, simulation
models, and video analysis. [El-Basyouny and
Sayed, 2013, Boroujerdian, Karimi and Seyed
abrishami, 2014]. The data collection by
observers may be accompanied by an error [Lu et
al. 2012]. Also, simulation models do not account
for the diverse and less predictable driver
behaviour that exists in real road traffic. Because
of the major limitations associated with collecting
conflict data through field observers and
simulation models, video analysis is a useful
method to analyse driving behaviour at
microlevel [Autey, Sayed, and Zaki, 2012, El-
Basyouny and Sayed, 2013].
In this study, traffic data were collected using a
digital camera fixed on a building near the
intersection. The entrance traffic volume to the
major approaches is between 600 and 1100 v/h
and this volume for minor approaches is between
200 and 450 v/h. The composition of the
different types of vehicles includes 61%
passenger cars, 38% motorcycle, and 1% of other
vehicles (heavy vehicles and van) in major
approaches and 54% passenger cars, 36%
motorcycle and 10% of other vehicles in minor
approaches. For this study, 353 cases, including
left-turning movements from minor to major
approaches were extracted from videos.
3.2 Data Processing
In this study, the video analysis is used for the
analysis of the driving behaviour. Data are
analyzed with Kinovea software that is the open-
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source software.This software is a video player
for the movement analysis. It provides a set of
tools for microscopic analysis of a video that
gives movement characteristics, including the
coordinates and the speed of the movement. For
the analysis of left-turning movement, first, the
vehicles coordinates in the pixels are converted to
the real coordinates in road side by the camera
calibration. Then, the vehicles are tracked by the
software. Vehicle tracking is performed at 0.04 s
intervals. The location of the vehicles and their
speed are obtained and smoothed. Then, the
speed profiles of left-turning vehicles are plotted
on their movement trajectories. Figure 2 shows
the process of drawing the speed profiles.
Figure 2. Process of drawing speed profiles
The plotted speed profiles are categorized based
on the shape of the speed profiles. For this, it is
used a qualitative evaluation. The shape of speed
profiles is categorized based on the speed
variations. To evaluate influence factors on the
choice of the speed profiles type, five explanatory
variables are considered that include the type of
left-turning vehicle (taxi and other vehicles),
initial speed of left-turning vehicle, its exposure
with the vehicles from left approach, the exposure
with the vehicles from right approach and the
exposure with the vehicles from opposite
approach. Then, an MNL model is developed for
choosing the speed profiles. An MNL model is
one of the discrete choice models that it is used
when there are more than two alternatives for
choice. In this study, there are three types of
speed profiles as alternatives which are the
discrete data, thus an MNL model is selected for
the choice of the speed profile types. The general
form of the MNL model is defined as follows:
Tracking of
left turning
vehicle
Smoothing of
movement
trajectory
Vehicle’s
speed profile
Drawing of
speed profile
on the
movement
trajectory
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
International Journal of Transportation Engineering,
Vol. 8/ No.2/ (30) Autumn 2020
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jiJij
V
Vob
J
j
j
ii
,...,,...,1;
exp
expPr
1 (1)
Where:
Probi= probability of an individual choosing
alternative i out of the set of J alternatives,
Vi= observed utility index for alternative i,
Vj= observed utility indices for all J.
alternatives.
And utility function is defined as follows
[Hensher, Roseand Greene, 2005]:
)(...)()()( 3322110 kikiiiiiiiii XfXfXfXfV
(2)
Where:
Xki= observed choice attributes and individual
characteristics
βki = parameter associated with attribute Xk and
alternative i,
β0i = a parameter not associated with any of the
observed and measured attributes, called the
alternative specific constant, which represents on
average the role of all the unobserved sources of
utility.
After determining the utility functions, sensitivity
analysis is performed based on the calculated
probability of the choice of the speed profile
employing equation (1).
4. Data Analysis
4.1 Categorizing Speed Profiles Based on
Their Shapes
The speed profiles are categorized into three
types based on their shapes. For this, The speed
profile of each vehicle extracted from videos and
then a qualitative evaluation is used to define the
speed profiles. The surveying of the trend of
speed variations is indicated three categories of
speed profiles. The types of speed profiles are
shown in Figure 3.
Figure 3. Types of speed profiles in the case study
Types (A) and (B) speed profiles exhibit a
descending slope first, followed by an ascending
slope. The difference between Types (A) and (B)
speed profiles is that type (B) speed profile has a
smoother slope than type (A) speed profile. Also,
type(C) speed profile has a consistently
ascending slope.
4.2 Influential Variables on Speed
Profiles
Among total speed profiles, 48%, 27%, and 25%
belong to type (A), type (B) and type (c),
respectively.
4.2.1 Vehicle Type Variable
It is hypothesized that the taxi drivers have
different driving behaviours compared to the
drivers of other vehicles. One possible
explanation can be that taxi drivers spend more
time on driving during a day than drivers of other
vehicles. Therefore, taxi drivers are considered as
the most experienced drivers and compared with
usual drivers. As a result, the type of left-turning
vehicle(taxi versus other vehicles) is selected as a
variable in this study. Figure 4 shows speed
profile types belonging to taxis and other
vehicles.
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Figure 4.The percentage of speed profiles types in
taxi and other vehicles
The results indicate that the choice of the speed
profile is not affected by the vehicle type.
4.2.2 Initial Speed Variable
Investigation of the effect of initial speed of left-
turning vehicle on the choice of the speed profile
shows that many drivers who choose types (A)
and (B) speed profiles have the initial speedover
10 km/h while most of the drivers who choose
type (C) speed profile have the initial speed less
than 20 km/h.
Figure 5.Ranges of the initial speed of vehicles in
each speed profile category
It can be concluded that the drivers with higher
initial speed tend to select a speed profile with a
descending slope and then an ascending slope.
Also, the collected data show that the highest
percentage of maximum initial speed occurred in
type (B) speed profile, while the percentage of
minimum initial speed in type (C) was higher
than the other two types.
4.2.3 Exposures Variable
There is a hypothesis that when a driver sees a
exposure, this affects his/her movement to avoid
an accident.
In this study, for investigation of the influence of
the exposures with left-turning vehicles on the
choice of the speed profile type, two states are
considered including the exposure from all
approaches with left-turning vehicles and cases
without any exposure as shown in Figure 6.
Figure 6. Distribution of speed profile types based
on exposures from approaches
The evaluation indicated that 70% of the left-turn
movements that have exposures with the vehicles
from all other approaches exhibit type (A) speed
profile, while 66% of left-turning vehicles
without any exposures show type (C) speed
profile. It indicates that the drivers choose type
(C) speed profile in the scenarios with less risk
and increase their speed when crossing the
intersection.
4.3 Developing a choice model of speed
profiles in left-turning movement
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
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As mentioned above, speed profiles are
categorized into three types. To develop a choice
model, from each of left-turning observations,
five explanatory variables are extracted that
include the type of left-turning vehicle (taxi
versus other vehicles), the initial speed of the left-
turning vehicle (speed before arrival at the
intersection) and possible exposures from one of
the other three approaches. The vehicle type and
the exposures from other approaches variables
are defined as binary variables. If the vehicle type
variable is a taxi thus it has a value of 1 and else
0. Also, if there is a exposure from each of the
directions, the exposure variable has a value of 1
and else 0. Meanwhile, the initial speed variable
is considered as a continuous variable.
An MNL model is used to explain how drivers
choose their speed profile in left-turning
movement. Utility functions for the speed profile
are defined as follows:
WwRrSpeedsTypeCU
SpeedscTypeBU
LlcTypeAU
CCC
BB
AA
...)(
.)(
.)(
.
(3)
Where:
U(TypeA) = utility of type (A) speed profiles,
U(TypeB) = utility of type (B) speed profiles,
U(TypeC) = utility of type (C) speed profiles,
Speed= the initial speed of left-turning vehicle
(km/h),
L = the exposure with the vehicles from left
approach,
R = the exposure with the vehicles from right
approach,
W = the exposure with the vehicles from
opposite approach,
cA, lA, cB, sB, sC, rC and wC= MNL model
parameters.
The model is estimated using N-Logit software.
The results of the estimated model are presented
in Table 2.
Table 2. Results of the estimated model
Type of Speed
Profile Variable Coefficient
Std.
Error
P value
(sig.)
Type (A) Intercept -3.44949 0.58498 0.0000
Exposure with vehicles from left major approach 1.51001 0.23494 0.0000
Type (B) Intercept -6.15867 0.76390 0.0000
Initial speed 0.15447 0.03192 0.0000
Type (C)
Initial speed -0.14704 0.03128 0.0000
Exposure with vehicles from right major approach -1.06499 0.28933 0.0002
Exposure with vehicles from opposite minor approach -1.04792 0.29407 0.0004
Number of Observation=353
Log Likelihood=-296.82569
AIC/N=1.721
Chi-Squared=151.09104
ρ2=0.203
ρc2=0.190
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4.3.1 Modelling Results
The results of the estimated model show that each
of the coefficients of the explanatory variables is
significantly different from zero. The p-values of
these variables are significant at the 99%
confidence interval (p < 0.0001) as shown in
Table 2. Also, the chi-squared test of
overall significance indicates that the model is
significant at the 99% confidence interval (chi-
squared < value, degree of freedom=5).
This model shows that the exposure of left-
turning vehicles with the vehicles from left major
approach increases the probability of Choosing
type (A) speed profile. The results show that the
probability of choosing type (B) speed profile is
increased by the increase of the initial speed. The
model indicates that if the vehicle has a slower
initial speed and there is not any vehicle in right
major and minor opposite approach, the
probability of choosing type (C) speed profile is
increased.
5. Model Sensitivity Analysis
And Interpretation
The sensitivity analysis of the impact of the
explanatory variables on the probability of the
choice of the speed profiles is conducted. For
evaluation of the influence of the initial speed and
the exposures on the choice behaviour of the
speed profiles by the drivers, eight hypothetical
exposure scenarios are considered as shown in
Figure 7.
Figure 7. Hypothetical exposure scenarios
In each of the scenarios, the probability of the
choice of each of the speed profiles is calculated
at different initial speeds as shown in Figure 8.
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Figure 8. The choice probability of the speed
profiles dependent on the initial speed and the
exposure type
It is hypothesized that the drivers whose initial
speed is low check the traffic conditions of the
intersection before arriving at the intersection
and after the finding the crossing priority, cross
the intersection with increasing the speed thus, in
the condition that there is not any exposure as
illustrated in scenario 8 of Figure 8, the choice
probability of type (C) speed profile is higher
than the choice probability of other profile types
at low to medium initial speeds. At medium to
high speeds, while there is not any exposure, the
choice probability of type (B) speed profile is
higher than the choice probability of other
profiles. In this condition, the drivers cross the
intersection with confidence hence they increase
their speed but also decrease their speed slightly
in the middle of the intersection for more caution
because of feeling high risk. By creating the
exposure from an approach, the choice
probability of type (C) speed profile is decreased.
In scenarios 2 and 3 in which there is a exposure
from the right and opposite approach,
respectively the choice probability of type (C)
speed profile is higher than other profile types at
low to medium speeds and the choice probability
of type (B) speed profile is higher than other
profiles at medium to high speeds. Also, the
choice probability of type (A) speed profile is
increased rather than scenario 8 because the
probability of the braking is increased with the
existence of the exposure; however, the choice
probability of type (A) profile is less than the
choice probability of other profiles. In scenario 1,
there is a exposure from the left approach. In this
state, the choice probability of type (C) speed
profile is higher than the choice probability of
other profiles at low initial speeds while at
medium initial speeds, the choice probability of
type (A) speed profiles is higher than the choice
probability of other profiles. Because in this
scenario, the drivers pay attention to their left
direction and they react with more focus on the
left exposure. At high initial speeds, the choice
probability of type (B) speed profiles is higher
than the choice probability of other profiles. The
choice of type (B) speed profile at high speeds
Analysis of Speed Profiles at An Unsignalised Intersection for Left Turning Vehicles
International Journal of Transportation Engineering,
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despite the existence of the left exposure shows
that the drivers are aggressive and they do not
tend to decrease their speed so much. In scenario
4, the choice probability of type (C) speed profile
is higher than other profiles at low initial speed.
At medium initial speed, the choice probability
of type (A) speed profile is higher than other
profiles and the drivers exercise caution more
than scenario 8, 2 and 3 and they prefer to brake
for more numbers of the exposures and the
information volume that they should process. The
choice probability of type (B) speed profile is
higher than other profiles at high initial speeds.
At this range of speed, the drivers do not tend to
decrease their speed and they might be
aggressive drivers. In scenarios 5 and 6, similar
to scenario 4, there are exposures from two
directions, one from the left and the other from
right or opposite direction. . For left-turning
movement, the drivers pay attention to the left
more than other directions and they brake for
more caution thus the choice probability of type
(A) speed profiles is higher than other profiles at
low to medium initial speeds. At medium to high
speeds similar to scenario 4, the choice
probability of type (B) speed profile is higher
than other profiles. In scenario 7, for the
exposures from all approaches, the drivers
exercise more caution than other scenarios
therefore the choice probability of type (A) speed
profile is higher than other profiles at low to
medium initial speeds. At medium to high speeds,
the choice probability of type (B) speed profile is
higher than other profiles. This indicates that in
spite of the high level of initial speed and the
exposures from all approaches, the drivers choose
type (B) speed profiles, which might state that
they are aggressive.
6. Discussion and Conclusions This paper presents a method that uses a two-step
analysis to determine driving behaviour while
crossing the intersection: 1.Categorizing the
speed profiles, 2.Developing the MNL model for
the choice of the speed profile. The mentioned
intersection is a case study to indicate the process
of implementing the suggested method to
determine driving behaviour.
For this purpose, the speed profiles of left-turning
vehicles at the unsignalised intersection are
categorized into three types. Types (A) and (B)
speed profiles show a descending initial slope
followed by an ascending slope. The difference
between Types (A) and (B) speed profiles is that
type (B) is smoother than type (A) speed profile.
Also, type (C) speed profile has a consistently
ascending slope. This research shows that among
353 left-turning vehicles, about 50% of the speed
profiles belong to type (A). Also, the percentage
of the choice from each of the speed profile types
is almost equal for taxi drivers and other vehicle
drivers in a left turning movement. Evaluation of
the initial speed indicated that most of the drivers
who choose type (A) and type (B) speed profiles
have an initial speed of more than 10 km/h, while
most of the drivers who choose type (C) speed
profile have the initial speed of less than 20 km/h.
In 70% of the cases where the left turning vehicle
has exposures with the vehicles from the other
three approaches, type (A) speed profile is
observed. Also in about 70 % of the cases that
there are not any exposures, the left turning
vehicle has type (C) speed profile.
After determining the categories of the speed
profiles, the MNL model is used for the choice of
these profiles. The model shows that such choice
is depended on the initial speed and the exposures
from other approaches.
Then, the sensitivity analysis is conducted for the
evaluation of impact of the explanatory variables
on the probability of the choice of the speed
profiles. The results of these analyses indicate
that the increasing number of exposures and the
existence of the left exposure increase the
drivers’ tendency to choose type (A) speed
profile at low to medium speeds. But when the
Maryam Dolatalizadeh, Amin Mirza Boroujerdian, Seyed Ehsan Seyed Abrishami
International Journal of Transportation Engineering,
Vol. 8/ No.2/ (30) Autumn 2020
162
initial speed is high, most drivers cross the
intersection with type (B) speed profile in all
scenarios. It can be dangerous especially when
the number of the exposures is high. In this
condition, the methods such as the traffic calming
can contribute to the safety of the intersection.
Also, low initial speeds and low numbers of the
exposures enhance the probability of the choice
of type (C) speed profile.
Practical applications of this research can be
followed as:
1. The extraction of the behavioral model of
drivers in left-turning movement at
unsignalized intersection is very
important in micro-simulation models
and as various intersections may have
different behavioral models, this study
present a simple method to extract a
behavioral model for such intersections.
2. The identification of drivers’ behaviour
in left turning will improve the
parameters needed to calibrate
simulation models at an unsignalised
intersection that can be used to study
safety or traffic at the intersection.
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